"Almost flat" simplices in Riemannian manilfolds

Stefan von Deylen

Given points in a Riemanian manifold, the "Riemannian centre of mass" is a way to introduce barycentric coordinates, mapping the Euclidean standard simplex into the manifold. We have shown that its distortion properties, if the standard simplex is equipped with a flat metric defined by geodesic edge lengths, is similar to normal coordinates.